M. Mahdavi-Hezavehi: Tits Alternative for Maximal Subgroups of $GL_n(D)$

mahdavih@sharif.edu

Submission: 2003, Oct 5

Let $D$ be a noncommutative division algebra of finite dimension over its centre $F$. Given a maximal subgroup $M$ of $GL_n(D)$ with $n \geq 1$, it is proved that either $M$ contains a noncyclic free subgroup or there exists a finite family $\{K_i\}^r_1$ of fields properly containing $F$ with $K^*_i\subset M$ for all $1\leq i\leq r$ such that $M/A$ is finite if $Char F = 0$ and $M/A$ is locally finite if $Char F = p>0$, where $A=K^*_1 \times \cdots \times K^*_r$.

2000 Mathematics Subject Classification: 15A33, 16K

Keywords and Phrases: Free Subgroup, Division ring, maximal subgroup

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